American Plum, Wild Plum - Prunus americana

Prunus americana - American Plum, Wild Plum. Threatened in New Hampshire and Vermont.
Shrub to small tree growing up to 25' tall, and can be nearly as wide. It has low branches and thorns up to 3" long, so in the wild it can be part of a nearly impenetrable thicket.
The fleshy fruit is edible. The plum fruit is usually around an inch in diameter.

Update 04/02/2014: I've been advised by Richard Ware of the Georgia Botanical Society, a man with expertise in trees FAR beyond my own, that this is a persimmon (Diospyros virginiana) rather than a plum (Prunus americana).